[GAP Forum] what is the difference between Conway Polynomial and minimal polynomial?

[Thomas Breuer]

Dear Shen,

the information you ask for can be obtained from the GAP Reference Manual.
In a GAP session, you can ask for help about the GAP function
'ConwayPolynomial' by entering

    ?ConwayPolynomial

at the GAP prompt.

The manual section about this function contains the definition of
Conway polynomials.
You will find there that Conway polynomials are the minimal polynomials
of very special elements in finite fields,
but not every minimal polynomial of a field element is a
Conway polynomial.

All the best,
Thomas


On Sat, Mar 14, 2015 at 08:59:28AM +0000, shengyu shen wrote:
> Dear all:
> 
> I am learning GAP, and I find that the Conway Polynomial is somewhat similar to minimal polynomial, because both will be used to construct the extension field.
> 
> So is there any difference?
> 
> Furthermore, the gap command  ConwayPolynomial( 2, 5 ) directly return a polynomial, but I think there may be many different minimal poly for the same p and n. So which one will be chosen to be ConwayPolynomial?
> 
> 
> Shen